Electron-transfer reactions Marcus theory

Key words Electron-transfer reactions - Marcus theory - Solvent fluctuations - Free-energy barriers -Inverted region... 

Equation (5-69) is an important result. It was first obtained by Marcus " in the context of electron-transfer reactions. Marcus derivation is completely different from the one given here. In electron transfer from one molecule (or ion) to another, no bonds are broken or formed, so the transition state theory does not seem to be applicable. Marcus assumed negligible orbital overlap in the electron-transfer transition state, but he later obtained the same equation for group transfer reactions requiring significant overlap. Many applications have been made to proton transfers and nucleophilic displacements. ... 

Eig. 2. Electron-transfer reaction rate, vs exoergicity of reaction the dashed line is according to simple Marcus theory the soUd line and data poiats are... 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

R. A. Marcus (California Institute of Technology) contributions to the theory of electron transfer reactions in chemical systems. 

R. A. Marcus, Electron-transfer reactions in chemistry - theory and experiment (Nobel Lecture), Angew. Chem. Int. Ed. 1993, 32, 1111. 

Marcus RA (1965) On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J Chem Phys 43 679... 

Marcus, R., Electron transfer reactions in chemistry theory and experiment. In Protein Electron Transfer (1996), Bendall, D., Ed., BIOS Scientific Oxford, pp. 249-272... 

Table 6.6 lists some reactions of the electron in water, ammonia, and alcohols. These are not exhaustive, but have been chosen for the sake of analyzing reaction mechanisms. Only three alcohols—methanol, ethanol, and 2-propanol—are included where intercomparison can be effected. On the theoretical side, Marcus (1965a, b) applied his electron transfer concept (Marcus, 1964) to reactions of es. The Russian school simultaneously pursued the topic vigorously (Levich, 1966 Dogonadze et al, 1969 Dogonadze, 1971 Vorotyntsev et al, 1970 see also Schmidt, 1973). Kestner and Logan (1972) pointed out the similarity between the Marcus theory and the theories of the Russian school. The experimental features of eh reactions have been detailed by Hart and Anbar (1970), and a review of various es reactions has been presented by Matheson (1975). Bolton and Freeman (1976) have discussed solvent effects on es reaction rates in water and in alcohols. 

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

In our description of the Marcus theory of electron-transfer reactions we have found it helpful to plot the free energy change in the three dimensional picture shown in Fig. 10 (Albery, 1975c, 1980). This picture emphasizes that... 

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